Question

the hot air balloon starts descending from an elevation of 2,400 feet. it descends at a constant rate of 400 feet per minute. now, write an equation that represents this line. you can represent the elevation of the balloon with the variable e. show that now. the slope is -400. the vertical intercept is 2,400. \\(\square =? +?\\) \\(\text{elevation} = \text{starting elevation} + \text{change in elevation}\\) \\(t\\) \\(e\\)

Explanation:

Step1: Identify linear equation form

The relationship follows the slope-intercept form of a line: $y = mx + b$, where $m$ is the slope, and $b$ is the vertical intercept.

Step2: Assign variables and values

Here, elevation $e$ is the dependent variable, time $t$ (minutes) is the independent variable. The slope $m = -400$ (rate of descent), vertical intercept $b = 2400$ (starting elevation).

Step3: Substitute into equation

Replace $y$ with $e$, $m$ with $-400$, $x$ with $t$, and $b$ with $2400$.
$e = -400t + 2400$

Answer:

$e = 2400 - 400t$ (or $e = -400t + 2400$)